Critical point equation on $K$-contact generalized Sasakian space form
UDC 514.7 We investigate the critical-point equation within the framework of $K$-contact generalized Sasakian space forms. It is demonstrated that a complete $K$-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere $S^{2n+1...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9409 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 514.7
We investigate the critical-point equation within the framework of $K$-contact generalized Sasakian space forms. It is demonstrated that a complete $K$-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere $S^{2n+1}$. In addition, we show that if this space form satisfies the Euler–Lagrange equation corresponding to the total scalar curvature functional, then it is Einstein and also satisfies the Fischer–Marsden equation. An illustrative example is provided to support and validate our theoretical findings. |
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| DOI: | 10.3842/umzh.v78i3-4.9409 |